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The p-restricted edge-connectivity of Kneser graphs

Author

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  • Balbuena, C.
  • Marcote, X.

Abstract

Given a connected graph G and an integer 1 ≤ p ≤ ⌊|V(G)|/2⌋, a p-restricted edge-cut of G is any set of edges S ⊂ E(G), if any, such that G−S is not connected and each component of G−S has at least p vertices; and the p-restricted edge-connectivity of G, denoted λp(G), is the minimum cardinality of such a p-restricted edge-cut. When p-restricted edge-cuts exist, G is said to be super-λp if the deletion from G of any p-restricted edge-cut S of cardinality λp(G) yields a graph G−S that has at least one component with exactly p vertices. In this work, we prove that Kneser graphs K(n, k) are λp-connected for a wide range of values of p. Moreover, we obtain the values of λp(G) for all possible p and all n ≥ 5 when G=K(n,2). Also, we discuss in which cases λp(G) attains its maximum possible value, and determine for which values of p graph G=K(n,2) is super-λp.

Suggested Citation

  • Balbuena, C. & Marcote, X., 2019. "The p-restricted edge-connectivity of Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 258-267.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:258-267
    DOI: 10.1016/j.amc.2018.09.072
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    References listed on IDEAS

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    1. Wang, Shiying & Ma, Xiaolei, 2018. "The g-extra connectivity and diagnosability of crossed cubes," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 60-66.
    2. Yang, Da-Wei & Feng, Yan-Quan & Lee, Jaeun & Zhou, Jin-Xin, 2018. "On extra connectivity and extra edge-connectivity of balanced hypercubes," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 464-473.
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